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Elementary math utilities with a focus on random number generation, non-linear optimization, interpolation and solvers

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/*
 * Copyright 2013 Stefan Zobel
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 *     http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 */
package math.distribution;

/**
 * The Exponential(λ) distribution for x >= 0 with PDF:
 * 
 * f(x; λ) = λ * e^{-λ * x} where λ
 * > 0.
 * 

 * Valid parameter ranges: x >= 0; λ > 0.
 * 
 * See
 * Wikipedia
 * Exponential distribution.
 */
public class Exponential implements ContinuousDistribution {

    private static final double BIG = 100.0;

    private final double lambda;

    public Exponential(double lambda) {
        if (lambda <= 0.0) {
            throw new IllegalArgumentException("lambda <= 0.0 : " + lambda);
        }
        this.lambda = lambda;
    }

    @Override
    public double pdf(double x) {
        return x < 0.0 ? 0.0 : lambda * Math.exp(-lambda * x);
    }

    @Override
    public double cdf(double x) {
        if (x <= 0.0) {
            return 0.0;
        }
        double y = lambda * x;
        if (y >= BIG) {
            return 1.0;
        }
        return -Math.expm1(-y);
    }

    @Override
    public double inverseCdf(double probability) {
        if (probability <= 0.0) {
            return 0.0;
        }
        if (probability >= 1.0) {
            return Double.MAX_VALUE;
        }
        return -Math.log1p(-probability) / lambda;
    }

    @Override
    public double mean() {
        return 1.0 / lambda;
    }

    @Override
    public double variance() {
        return 1.0 / (lambda * lambda);
    }
}